Finite Math Examples

$z = 2 x + 4 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $2 x + 4 y = z$ .

$2 x + 4 y = z$

Step 1.2

Subtract $2 x$ from both sides of the equation.

$4 y = z - 2 x$

Step 1.3

Divide each term in $4 y = z - 2 x$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = z - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{z}{4} + \frac{- 2 x}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{z}{4} + \frac{- 2 x}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{z}{4} + \frac{- 2 x}{4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $- 2$ and $4$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $- 2 x$ .

$y = \frac{z}{4} + \frac{2 (- x)}{4}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $4$ .

$y = \frac{z}{4} + \frac{2 (- x)}{2 (2)}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{z}{4} + \frac{2 (- x)}{2 \cdot 2}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{z}{4} + \frac{- x}{2}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = \frac{z}{4} - \frac{x}{2}$

Step 2

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

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Step 3.1

Remove parentheses.

$y = \frac{1}{4} - \frac{0}{2}$

Step 3.2

Simplify $\frac{1}{4} - \frac{0}{2}$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Divide $0$ by $2$ .

$y = \frac{1}{4} - 0$

Step 3.2.1.2

Multiply $- 1$ by $0$ .

$y = \frac{1}{4} + 0$

Step 3.2.2

Add $\frac{1}{4}$ and $0$ .

$y = \frac{1}{4}$

Step 3.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(0, \frac{1}{4}, 1)$

Step 4

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

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Step 4.1

Remove parentheses.

$y = \frac{2}{4} - \frac{1}{2}$

Step 4.2

Simplify $\frac{2}{4} - \frac{1}{2}$ .

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Step 4.2.1

Cancel the common factor of $2$ and $4$ .

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Step 4.2.1.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{4} - \frac{1}{2}$

Step 4.2.1.2

Cancel the common factors.

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Step 4.2.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 1}{2 \cdot 2} - \frac{1}{2}$

Step 4.2.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 2} - \frac{1}{2}$

Step 4.2.1.2.3

Rewrite the expression.

$y = \frac{1}{2} - \frac{1}{2}$

Step 4.2.2

Combine the numerators over the common denominator.

$y = \frac{1 - 1}{2}$

Step 4.2.3

Simplify the expression.

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Step 4.2.3.1

Subtract $1$ from $1$ .

$y = \frac{0}{2}$

Step 4.2.3.2

Divide $0$ by $2$ .

$y = 0$

Step 4.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(1, 0, 2)$

Step 5

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

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Step 5.1

Remove parentheses.

$y = \frac{3}{4} - \frac{2}{2}$

Step 5.2

Simplify $\frac{3}{4} - \frac{2}{2}$ .

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Cancel the common factor.

$y = \frac{3}{4} - \frac{2}{2}$

Step 5.2.1.1.2

Rewrite the expression.

$y = \frac{3}{4} - 1 \cdot 1$

Step 5.2.1.2

Multiply $- 1$ by $1$ .

$y = \frac{3}{4} - 1$

Step 5.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{3}{4} - 1 \cdot \frac{4}{4}$

Step 5.2.3

Combine $- 1$ and $\frac{4}{4}$ .

$y = \frac{3}{4} + \frac{- 1 \cdot 4}{4}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{3 - 1 \cdot 4}{4}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 1$ by $4$ .

$y = \frac{3 - 4}{4}$

Step 5.2.5.2

Subtract $4$ from $3$ .

$y = \frac{- 1}{4}$

Step 5.2.6

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 5.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(2, - \frac{1}{4}, 3)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{1}{4}, 1), (1, 0, 2), (2, - \frac{1}{4}, 3)$